The images you take with your real CCD camera, your real telescope, under our very real atmosphere of swirling gases are 'corrupted' by many processes. This shows up most simply in star images. Stars are essentially point sources but real images are not points. On your video monitor they appear as (more or less) circular disks. If you use the Profile function, you can see that the images can be likened to 'hills' or 'piles' of electrons. The total result of imaging point sources such as stars is known as the point spread function (PSF).
In theory, and in practice to a limited extent, knowledge of the PSF can be used to estimate what the image would have looked like in the absence of all those corrupting influences. The Deconvolution Filter uses an iterative form of a Wiener filter to produce such an estimate from your data.
Iterative means you have to try it over and over until you are satisfied. The process is as much art as science and you will need to develop some intuitive skills and will need to work with the very best images you can muster. Very best is measured in terms of low noise, which means sufficient exposure to have high signal to noise ratios and good calibration in terms of flat fielding.
The Deconvolution Filter starts with an estimate of the 'ideal' image, convolves it with a Gaussian function using parameters you supply from the image to get a 'prediction' of the real image. This predicted image is compared with the real image and any differences are subtracted from the estimated image to get a new estimate. The process is repeated by the number of times you select, and each time the errors tend to get smaller so that, at the end, you can say something like
IF the true PSF is similar to the Gaussian function used in this process, THEN the estimated ideal image MUST be pretty close to the real ideal scene that produced the actual image I have in my camera.
In practice, you will get sharper star images, will separate some double stars that were a common blur and will see some improvement in resolution of extended objects (VERY dependent on the initial quality of your images).
JIMSAIP uses the image itself as the starting estimate (in Buffer A). It will ask you for the FWHM in the row direction and in the column direction. You can get starting numbers for these data from the Profile Function in the Examine mode. It will use these data to construct an idealized Gaussian PSF for use in the convolution process. Note that by using different values for the row and column directions, you can remove some of the distortions resulting from poor tracking. It will also ask you for a background noise value which you can get in the Examine mode by putting the box cursor in an empty part of the image and reading the average value from the displayed data.
Next, JIMSAIP will ask you for the number of iterations you want to run. Clearly, the time needed for the procedure will depend on this number (and on your computer's speed and the size of the image - there is a LOT of computation involved in this procedure). It is surprising, however, how much improvement you can get in only three iterations.
After receiving the needed data, JIMSAIP will perform the operation. Percentage bars keep you informed of the progress. When the procedure is completed, JIMSAIP puts the estimated 'ideal' image in Buffer A (which it displays). In Buffer B is the original image (less the noise background you entered), and the predicted image using the estimated 'ideal' image and the best-guess PSF is in Buffer C.
You can flip among the three images using the A, B, and C keys to compare results. In particular, you should compare the B and C images to see how similar they are. If you determine that the star images in C are wider or higher than those in B, you can infer that you have used a PSF (derived from the FWHM you entered) that is too large in the respective direction. You can run the process again with better estimates. (Note that you can copy the image in B to the A buffer and use zero for the background noise estimate - because you already subtracted it out in the previous iteration.) As the process will raise the peak values for the star images (use the Profile function to verify this, you can adjust BLACK and WHITE levels of the A image to get a more pleasing view.